1898 - 99 .] Prof. Tait on Linear and Vector Function. 549 
Another portion of the paper deals with a sort of converse of 
the above problem : — The relation between two strains (whether 
with three real roots or with one) when their successive applica- 
tion gives a pure strain ; and various questions of a similar kind. 
In these inquiries we constantly meet with a somewhat puzzling 
form, which repeats itself in a remarkable manner under the usual 
modes of treatment, viz. : — 
<oY €p + V eo)p . 
A little consideration, however, shows that it can be put into 
the form 
V(m 2 e — ooe)p 
which is thoroughly tractable. 
